Q1. A steel wire of cross-sectional area 3 x 10- 5m2 and length of Sm stretches by the same length as

a copper wire of cross-sectional area 4.0 x ur5m2 and length 4m under a given load. Find the ratio of

Young's modulus of copper to that of steel?

Ans. Given, Length of the steel wire, L1 = 5 m

Cross-sectional area of the steel wire, A1 = 3.0 x 10-5 m2

Length of the copper wire, L2 = 4 m

Cross-sectional area of the copper wire, A2 = 4.0 x 10-5 m2

Change in length = /\.L 1 = /\.L2 = /\.L

Let the force being applied in both the situations = F

We know, Young's modulus of the steel wire

Y1 = (F1 I A1) (L1 I /\.L1)

= (FI 3 X 10-5) (51 /\.L) ......... _ ( 1 )

Also, Young's modulus of the copper wire·

Y2 = (F2 / A2) (L2 I /\.L 2)

= (FI 4 x 10·5) (3 I /\.L} ....... _ .. ( 2 )

Dividing equation ( 1 ) by equation ( 2 ), we get

Y1 /Y2 = (5x4x10-5) /(3x10•5x4)

= 1.6 1

The ratio of Young's modulus of steel to Young's modulus of copper is 1.6

Q2. The graph given below is the stress-strain curve of a material. Find this material's ( i

)Approximate yield strength ( ii) Young's modulus.

Ans.

300 ,::--250

� 200 �150

E 100 "' 50

0

_,,,'-' /

_/ '

_,,,v

I/

0 0.001 0.002 0.003 0.004 S1rnin

( i ) It can be seen from the graph that the approximate yield strength of this material is 300 x 106Nm/2or 3 x

108 N/m2.

( ii ) It is observed from the given graph that for strain O 001, stress is 75 x 106Nim2

.-. We know, Young's modulus, Y = Stress / Strain

= 75 x 1061 O 001 = 7 5 x 1010 Nm·2

QJ. Given below are stress-strain curves for two materials X and Y.

iCit_ Strain Strain

If both the graphs are drawn to the same scale.

(a) Identify the material with a greater Young's Modulus.

( b) Identify the stronger material.

Ans.

( a ) Comparing the two graphs we can infer that the stress on X is greater than that on Y for the same

values of strain. Therefore, Young's Modulus ( stress/strain ) is greater for X.

( b ) As X's Young's modulus is higher, it is the stronger material among the two. For strength is the measure

of stress a material can handle before breakinq_

NCERT SOLUTIONSCLASS-XI PHYSICS

CHAPTER-9MECHANICAL PROPERTIES OF SOLIDS